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A323433 Number of ways to split an integer partition of n into consecutive subsequences of equal length. 7
1, 1, 3, 5, 10, 14, 25, 34, 54, 74, 109, 146, 211, 276, 381, 501, 675, 871, 1156, 1477, 1926, 2447, 3142, 3957, 5038, 6291, 7918, 9839, 12277, 15148, 18773, 23027, 28333, 34587, 42284, 51357, 62466, 75503, 91344, 109971, 132421, 158755, 190365, 227354, 271511 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

FORMULA

a(n) = Sum_y A000005(k), where the sum is over all integer partitions of n and k is the number of parts.

EXAMPLE

The a(5) = 14 split partitions:

  [5] [4 1] [3 2] [3 1 1] [2 2 1] [2 1 1 1] [1 1 1 1 1]

.

  [4] [3] [2 1]

  [1] [2] [1 1]

.

  [3] [2]

  [1] [2]

  [1] [1]

.

  [2]

  [1]

  [1]

  [1]

.

  [1]

  [1]

  [1]

  [1]

  [1]

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0 or i=1, numtheory

      [tau](t+n), b(n, i-1, t)+b(n-i, min(n-i, i), t+1))

    end:

a:= n-> `if`(n=0, 1, b(n$2, 0)):

seq(a(n), n=0..50);  # Alois P. Heinz, Jan 15 2019

MATHEMATICA

Table[Sum[Length[Divisors[Length[ptn]]], {ptn, IntegerPartitions[n]}], {n, 30}]

CROSSREFS

Cf. A000005, A000219, A101509, A316245, A319066, A323295, A323300, A323307, A323429, A323434.

Sequence in context: A078411 A137630 A320886 * A220489 A229915 A092269

Adjacent sequences:  A323430 A323431 A323432 * A323434 A323435 A323436

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 15 2019

STATUS

approved

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Last modified January 28 03:28 EST 2020. Contains 331314 sequences. (Running on oeis4.)